Signed-negabinary-arithmetic-based optical computing by use of a single liquid-crystal-display panel
TL;DR: Based on the negabinary number representation, parallel one-step arithmetic operations (that is, addition and subtraction), logical operations, and matrix-vector multiplication on data have been optically implemented, by use of a two-dimensional spatial-encoding technique.
Abstract: Based on the negabinary number representation, parallel one-step arithmetic operations (that is, addition and subtraction), logical operations, and matrix-vector multiplication on data have been optically implemented, by use of a two-dimensional spatial-encoding technique. For addition and subtraction, one of the operands in decimal form is converted into the unsigned negabinary form, whereas the other decimal number is represented in the signed negabinary form. The result of operation is obtained in the mixed negabinary form and is converted back into decimal. Matrix-vector multiplication for unsigned negabinary numbers is achieved through the convolution technique. Both of the operands for logical operation are converted to their signed negabinary forms. All operations are implemented by use of a unique optical architecture. The use of a single liquid-crystal-display panel to spatially encode the input data, operational kernels, and decoding masks have simplified the architecture as well as reduced the cost and complexity.
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TL;DR: In this article, the authors argue that Keyes was and still is mostly correct, but that may change in a few years • Many researchers have indeed simply ignored what he said • New developments in both optical logic and its applications open niches for optical logic that Keye did not (and probably could not) anticipate • New and anticipated developments in electronics may increase the role for optics.
34 citations
26 Aug 2008
TL;DR: The overall computing time can be reduced to the sum of the time of flight through a very short optical path and the time needed for input and output.
Abstract: We propose a method for implementing digital-optical arithmetic with high accuracy at extremely high speed. To this end we use the superposition of photons running through a passive network of simple optical components. All possible solution are realized in parallel by superposition. Therefore, the overall computing time can be reduced to the sum of the time of flight through a very short optical path and the time needed for input and output.
11 citations
TL;DR: A nonlinear material-based all-optical switching mechanism is utilized here to realize the J-K and J- K master-slave (J-K M-S) flip-flops.
Abstract: A nonlinear material-based all-optical switching mechanism is utilized here to realize the J-K and J-K master-slave (J-K M-S) flip-flops. As the flip-flops are sequential logic circuits, the present states of outputs are dependent not only on the present inputs but also on the past outputs. In our present scheme, the outputs are fed back to the former stages as well as the input stages. The output of each flip-flop and its complement are obtained simultaneously in our scheme.
7 citations
01 Jan 2014
TL;DR: In this article, a nonlinear material based all-optical switching mechanism is utilized to develop the alloptical arithmetic operation scheme, where analog optical signals are converted to the corresponding digital signals by optical tree architectures.
Abstract: Nonlinear material based all‐optical switching mechanism is utilized here to develop the all‐optical arithmetic operation scheme. Analog optical signals are converted to the corresponding digital signals by optical tree architectures. First a four bit arithmetic unit has been accessed which is elevated to a higher bit arithmetic unit in course. These circuits can execute innumerable arithmetic operations and remarkably, as they are all‐optical and fully parallel in nature. These all‐optical arithmetic units can gear up to the highest capability of optical performance in high‐speed all‐ optical computers.
3 citations
TL;DR: This paper proposed Mach- Zender Interferometer (MZI) based tree-net architecture is used for the conversion scheme from binary number to modified trinary number in all-optical domain.
2 citations
Cites methods from "Signed-negabinary-arithmetic-based ..."
...So, to get carry-borrow free arithmetic operations various signed digit number systems have been described such as MSD (modified signed-digit), MMSD (mixed modified signeddigit), TSD (trinary signed digit), NTSD (non-recoded trinary signed digit) and negabinary signed-digit number system [2-10]....
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References
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TL;DR: An optical logic array processor is constructed that can implement parallel operations of addition or subtraction for two binary variables without considering the carry mechanism, and it is shown that the proposed method can be applied to combinational circuits.
Abstract: On the basis of a lensless shadow-casting technique, a new, simple method of optically implementing digital logic gates has been developed. These gates are capable of performing a complete set of logical operations on a large array of binary variables in parallel, i.e., the pattern logics. A light-emitting diode (LED) array is used as an incoherent light source in the lensless shadow-casting system. Sixteen possible functions of two binary variables are simply realizable with these gates in parallel by controlling the switching modes of the LED’s. Experimental results demonstrate the feasibility of various gate arrays, such as AND, OR, NOR, XOR, and NAND. As an example of application of the proposed method, we construct an optical logic array processor that can implement parallel operations of addition or subtraction for two binary variables without considering the carry mechanism. Use of the light-modulated LED array means that the proposed method can be applied to combinational circuits.
223 citations
TL;DR: Using residue arithmetic it is possible to perform additions, subtractions, multiplications, and polynomial evaluation without the necessity for carry operations.
Abstract: Using residue arithmetic it is possible to perform additions, subtractions, multiplications, and polynomial evaluation without the necessity for carry operations. Calculations can, therefore, be performed in a fully parallel manner. Several different optical methods for performing residue arithmetic operations are described. A possible combination of such methods to form a matrix vector multiplier is considered. The potential advantages of optics in performing these kinds of operations are discussed.
168 citations
116 citations
TL;DR: A new conditional symbolic substitution rule for modified signed-digit arithmetic computation is introduced, which is first replaced by a pair of new equivalent strings, which in a second step are subject to another substitution to generate both the addition or subtraction result and its complement.
Abstract: A new conditional symbolic substitution rule for modified signed-digit arithmetic computation is introduced. Using this substitution rule, the numbers to be added or subtracted are first replaced by a pair of new equivalent strings, which in a second step are then subject to another substitution to generate both the addition or subtraction result and its complement. For an optical implementation, a holographic contentaddressable memory is used. Correspondingly, the input encoding, the logic reduction, and the optical processing techniques are described.
110 citations
TL;DR: A novel high speed array processing optical architecture that provides a high speed means of matrix/vector multiplications using the digital multiplication via an analog convolution algorithm and a systolic acousto-optic implementation permit the speed of optics to be combined with the accuracy of digital computation.
Abstract: A novel high speed array processing optical architecture is described. A multichannel acousto-optic binary convolver is architecturally configured as a systolic array processor. The architecture provides a high speed means of matrix/vector multiplications using the digital multiplication via an analog convolution algorithm. This algorithm and a systolic acousto-optic implementation permit the speed of optics to be combined with the accuracy of digital computation.
86 citations